HW 6.1 why no conditional?

I think there where two ways to look at this question.

First: all transitions, in all 3 data sets where comparable, so you can calculate probability: count(A->A) / count(A -> X)

Second: there was a reason to split data into three data sets (ex. measurements were taken in different time intervals). So you should calculate: 1/3 * count(A1->A1) / count(A1->X1)

Why second interpretation is wrong?

Btw. i think that it would be nice, if there where little more emphasis on the subject of selecting correct models.